## Precalculus: Mathematics for Calculus, 7th Edition

First blank = $x^2 +2$ Second blank = $\frac{3x+6}{x^2 +2} + \frac{5x}{x^2+ 2} = \frac{2x^2 +4}{x^2 +2}$ OR... $\frac{8x+6}{x^2 +2} = \frac{2x^2 +4}{x^2 +2}$ (when simplfied)
First blank: The denominators consist of $x$, $x+2$, and $1$ (which is under $2$). The least common denominator would have to be $x^2 +2$ (because of $x$ and the $x-2$). Second blank: Multiply the first part by $x+2$, the second part by $x$, and the last part by $x^2 +2$. Combine the first and second parts (add) to your liking and you will have a resulting proportion.